A new kind of neural networks for continuously computing the shortest path problem is presented in this paper，and the stability of the network is proved．This kind of neural networks is composed of the minimum selecting networks and other usually used neurons．For any directed or undirected graph，the neural networks are always convergent to their single equilibrium,so that the shortest paths of all the node pairs are produced．This paper makes a new study on solving the optimization,but not NP—hard problems by neural networks．